# Finding the green's function for a second order linear DE and solve it

1. Sep 23, 2011

### storluffarn

1. The problem statement, all variables and given/known data

So I'm trying to get a grip about those Green functions and how to aply them to solve differential equations. I've searched the forums and read the section on green's functions in my course book both once and twice, and I think I start to understand at least som of it. However, all the cases treated in the litterature and most problems I found on the forums had boundary conditions on the form y(a)=q, y(b)=q. In the problem bellow I do not have these kind of boundary conditions.

"Construct the Green's function and apply it to solve the differential equation

$\frac{d^2 y(x)}{d x^2} -a^2 y(x) = e^{-t}$

subject to the boundary conditions y(0)=0, y'(0)=0

My question is this:

What do I do when the boundary conditions is in this form?

2. Relevant equations

-

3. The attempt at a solution

Well, I tried to see the situation as if y was bounded in the interval 0 to infinity, but that didn't work out to good. I also tried to formulate the equaton as a self adjoint, but that to failed.

Cheeres,
David

2. Sep 26, 2011

### storluffarn

Nvm, problem solved, thanks anyway!

3. Sep 26, 2011

### HallsofIvy

Staff Emeritus
Actually, that was a very strange question! All "Green's function" problems have those boundary conditions: y(0)= 0, y(L)= 0.